**Math
513, Au
2008**

Office hours: Monday and Friday, 11:00 a.m.- noon, and by appointment.

Tutoring offered at MSLC, Tuesdays 1-3 p.m.

**F Oct. 24 **

Topics: 3.2

Homework:

Write up the solutions and turn in for grading on Monday Oct. 27: 3.2: 1,2,3,4 (Note: this homework set is worth a maximum of 2 points.)

**M Oct. 27 **

Topics: 3.3

HW: Write up the solutions and turn in for grading on M Nov 3rd: 3.3: 2, 3, 4, 5, 6, 8, 10

**W Oct. 29 **

Topics: 3.4. Web resource: Divergence and Curl (© Copyright 2004-2007 Duane Nykamp.)

HW: Write up the solutions and turn in for grading on M Nov 3rd: **3.4**: 2, 4, 6, 7, 9, 12

**F Oct. 31 **

Topics: 3.5, From 3.7:Taylor series, the Hessian - see Examples 3.23, 3.24, 3.25. (No diadics.)

HW: Write up the solutions and turn in for grading on M Nov 3rd:** 3.5**: 4, 5, 6, 7, 8, **3.7**: 2, 3

**M Nov. 3rd **

Topics: 3.7 continued: the second derivative test (using the eigenvalues of the Hessian matrix).

Web resources: Multiplying matrices and vectors, Taylor's polynomials, Local extrema (pictures), Hessian matrix and the second derivative test

HW: Write up the solutions and turn in for grading on M Nov 10: **3.6**: the two problems below:

**A.** Find the critical points of the scalar field f(x,y,z)=(x+y-z)^2+y^2+z^2 and use the eigenvalues of the Hessian matrix to decide if these points are max, min, saddle.

**B.** Same questions for f(x,y,z)=x^2+y^2-z^2.

**W Nov. 5 **

Topics: 3.6

HW: Write up the solutions and turn in for grading on M Nov 10: **3.6**: 1, 2, 4, 5, 7, 8 **Note**: the* Laplacian of a vector field *is calculated by taking the Laplacian of each component (see the example on p.139 up).

**F Nov. 7 **

Topics: 4.1

HW: Write up the solutions and turn in for grading on M Nov 10:** 4.1: **2, 3, 4, 5, 11, 12, 14, 19, 20

Note: If you would like to have more time, you can turn in the homework on W Nov 12 (instead of M Nov 10).

**M Nov. 10 **

Topics: 4.2

HW: Write up the solutions and turn in for grading on M Nov 24 (after the midterm): For each of the following regions ( sketch them and) state and justify: 1) is it open? 2) is it closed? 3) What is its boundary? 4) Is is a domain? (Note: <= stands for "less or equal".)

**A**. 1<x^2+y^2<4 ; **B**. 1**<=**x^2+y^2<=4 ;** C. **1<x^2+y^2<=4 ; **D.** 0<x^2+y^2<4 ; **E**. |x|>=1 in the plane ;** F.** |x|>1 in space

**W Nov. 12 **

Topics: 4.2, start 4.3

HW: Write up the solutions and turn in for grading on M Nov 24 (after the midterm):** 4.2: **2 (see formula (D1) p 353), 4, 6, 7;

**F Nov. 14 **

Topics: 4.3

HW: Write up the solutions and turn in for grading on M Nov 24 (after the midterm):** 4.3**:1, 2a) c) e), 3a) c) e), 6, 7; Note: disregard a),c),e) in 3 (it is a typo).

**M Nov. 17 **

Topics: 4.4

HW: Write up the solutions and turn in for grading on M Nov 24 (after the midterm): **4.4**: 1a) c) e), 2, 4, 5, 6, 7

Special office hours: this W 11-12.

Extra practice problems: 4.4: 9b, 10. Read the text and work out the examples 4.7 (page 208), 4.8

**W Nov. 19 **

Review. See a Review guide for midterm 2.* Note:* midterm 2 covers problems similar to those in sections from 3.1 to 4.4. However, we need to use previous knowledge!

**F Nov. 21 ** Midterm 2

**M Nov. 24 **

Topics: Start 4.6

HW: Brush up calculation of double integrals using **COW**; choose the path 3.Calculus Book III > 5.Integration > 2.Double Integrals > Double integrals I

**W Nov. 26 **

Topics: 4.6, 4.7

HW: Write up the solutions and turn in for grading on M:** 4.6**: 2, 4, 5, 6, **4.7**: 2 a) c) g), 3, 5, 8, 11, 13, 15 **Also:** Review the calculation of triple integrals (you may use the link to COW).

**M Dec 1**

Topics: 4.8

HW: **4.8**: 1, 3, 4 a) b), 6

**W Dec 3** and **F Dec 5**

Topics: 4.9

HW: **4.9**: 1, 2, 3 b), 4, 8, 9, 12, 15, 17, 20.

Final examination info: You are allowed to bring and use one page (front and back) with *your own notes*. Here is a Review Guide. Please check the Final Exam Schedule.

I will be available on* Friday Dec. 12, from 11 a.m. to noon if you want to see your graded final exam.* However, I hope to have everything ready by Thursday, and if so, I will post here a time when I will be in my office on Thursday too.

Gibbs's lectures on Vector Calculus

**Undergraduate Research **

**JUROS** publication (for undergraduate research across disciplines).